Study On Oscillations Of Several Kinds Of Difference And Differential Equations

This thesis of Master is composed of four chapters, which mainly studied existence of positive solutions of higher-order nonlinear neutral difference equations, oscillation criteria for difference equations with impulses,linearized oscillation for odd-order neutral differential equations,existence of positive solutions of neutral differential equations with impulses.In chapter one, by using Banach contraction principle, we study existence of positive solutions of higher-order nonlinear neutral difference equations, and some sufficient conditions will be given.Chapter two mainly considers oscillation criteria for difference equations with impulses , some sufficient conditions will be given. Our main results improves and generalizes the some known results without Impulses ,which are new even for case without impulsive point.Chapter three mainly considers linearized oscillation for odd-order neutral differential equations , and some sufficient conditions will be established.In the last chapter, by using Banach contraction principle , we investigate existence of positive solutions of neutral differential equations with impulses.